Scale-type calculating device



Feb. 25, 1964 B. GRAHAM SCALE-TYPE CALCULATING DEVICE Filed July 23, 1962 gill m ugn- (II ILIIIP IH m m m In E T WW a r W w W W. mm 2 6 m l w D d a a uul L C m D United States Patent 3,122,314 SCALE-TYPE CALCULATKNG DEVHCE Benjamin Graham, dill N. Ma le Drive, Beverly Hills, Qaiii. Filed July 23, N62, Se No. Til/742 I 11 Claims. (6i. 235-61) This invention has to do generally with improvements in manually manipulated scale type calculators useable in general for making calculations for which slide rules are commonly employed.

My general objective is to provide a calculator which for at least many purposes and kinds of calculations, has

advantages over conventional slide rules by means of simpler and more easily understandable scale systems, and

greater'iacility and ac uracies in relating and determining values entering into and resulting from the calculations.

The invention is predicated upon the use of arithmetic scales, as distinguished fromlogarithmic scales, locations and values along which are more easily and accurately determinabiethan logarithmic values. Additionally, and in the interests of greater convenience, facility and visibility in manipulation, the present calculator employs a simple arrangement of scales, one on what may be merely a flat card-like base, and the other on a flat arm swingable on. the base. I

in its mathematical aspects, the invention is further predicated upon the use of corresponding scales on the arm.

and body, each constituting a dual arrangement of contiguous linear scales individually of arithmetically equal dimensions, with the two scales related in the ratio of the square root of 10. By employing a reference are about and intersectable by. the arm scales, the device operates on the mathematical principle of similar triangles, and by providingfor contiguous double scales having a greater and lesser numerical ranges, it is possible to achieve greaterreading accuracies in a device of given size, or-in other words, to reduce by half what otherwise would be the size required for comparable accuracy.

All the features and objects of the invention, as well as the details of certain typical andillustrativc embodiments, will be more fully understood from following description of the accompanying drawing, in which:

) 12 parallel to the diameter. The body carries what may be termed D scales paralleling the edge 12 and which may be imprinted directly on the base, or on a separately formed strip 13 flatly afiixcd to the base.

The D scales comprise a pair of onposed scales D and D;,, the former being a scale of 100 equal divisions between a marked or unmarked line l4 which is a projection of the center of pivot 15 normal to the straight edge 12, and the opposite extremity at numeral 100 which is a projection of the terminal of are 316 at its diameter through point l5, normal to the straight edge 12;. The two scales D and D are related by the ratio of the square root of 10, in that any value along the D scale is the square root of 10 times the corresponding value on the D scale, the latter therefor having values up to 31.62 at and corresponding to the 100' terminal ofthe D scale. As will be noted, the upper or D scale is divided into units and the D scale into fifths. The diameter of the circular are 16 and therefore the extents of both the arm and base D scales, may be of any desired length compatible with affording the desired accuracies and readability.

The body 10 also has marked or imprinted thereon an altitude line, designated Alt, which is perpendicular to the edge 12 and D scales and extends in alignment with the marking 10 on the D scale to intersection with the circular are 15. c

As previously mentioned, the calculator operates on the principle of similar triangles, and in this respect, the Alt. line forms one side of a triangle having its other sides along the A and D scale lines, as to also similar triangles having as their parallel counterpart of the Alt. line, the H or H line intersecting selected values on the A and D scales. The Alt. line intersects the D scale at 10 in order to provide for simple and, in effect, unity in one of the similar triangle values.

An arm 17, made in the form of a transparent strip, is pivoted to swing about the center 15 from a position, designated by the broken lines at l7a, of engagement or parallelism with the D scales or strip 13, to any of various calculating positions typified by FIGS. 1 and 2. The arm 17 ca :ies what may be termed a pair of A scales correspending exactly in length, divisions and their markings to the D scales, lo, the outer A scale being in exact correspondcnce with the D scale, and the inner A scale being I in exact correspondence with the D scale, excepting only that for convenience in use, the interval lines on the arm scales may be drawnat an appropriate angularity, say about 35 degrees, to the scale line. Because of limitations in calculating determinations occurring at the ends of the scales toward the pivot 15, markings may be there omitted and the scales started at substantially the values indicated.

device also uses a cursor or hairline carrier 13 which in the lFiGS. 1 and 2 embodiment of the invention may consist of a transparent strip carrying one or'more lines, e.g. H and ll the strip having a head l9 slidable along the straight edge 12 so that the hairlines are normal to the D scales and parallel to the Alt. line. Plural H lines may be used simply as a matter of convenience in limiting necessary shifting of thecursor. The cursor may be provided as a separate pi ce, and for convenience, the back side of the body lb may be provided with apocket, not shown, to accommodate the cursorwhen not in use.

The stated relationships in termsoi the square root of 10, between respectively the A A and the 13 ,13 scales, serves to provide for extended calculation range and ac-- in a calculation a value is selectedv at the A scale inter section with the are 16, to be related to an H or H selected value on the A scale, the, answer will appear at the intersection of the used H or H line with the D scale, by reason of its square root of 10 relation to the A scale and correspondence with the A scale. Similar relations and cancellation eiiects occur where selections are made on the D scales for answers reading in the A scales.

PEG. 3 illustrates a variational form of the invention similar to the described embodiment except the manner of accommodating the cursor as an attached component of the calculator. l-lerethe cursor it? is shown to be made in the form of a transparent strip carrying a pair of pro jections 21 which slide in a slot 22 extending throughthe body 235 in parallelism with the D scales so that, as before, the hairlines H, H extend pergiendicular to the D scale in the functional solid line position of the cursor. When not in use, the cursor may be slid to the left ex- 3,1 3 tremity of slot 22 and swung to the collapsed position indicated by broken lines 2%, as permitted by accommodation of the projections 21 within a quadrantal extension 220. of the slot.

The following are examples of various calculations in volving assured factors X and Y that can be made by simple manipulations of the device.

(1) To multiply X by Y Method A: Swing the arm A so that the outer scale A value for X falls on the arc 16. Place hairline H at Y on the inner arm scale A and read the answer under the hairline H on the lower D scale D FEG. 1 illustrates the calculations 8 (X) times 17 (Y) :136.

Method B: Swing the arm A so that X on the A scale falls on the Alt. line, place the hairline H at Y on the D scale and read the answer at the hairline intersection with the A scale.

2. To divide X by Y Method A: Swing the arm to its Y value at the A scale intersection with the arc 16. Place hairline H at X on the D scale and read the answer at the H intersection with the A scale.

Method B: Swing the arm to coincidence of Y on the A scale with Alt., place H over X on the A scale and read the answer below on the D scale.

Method C: Using the hairline H, swing X (or Y) whichever is of greater Value on the A scale perpendicularly above Y (or X) on the D scale and then read X/Y at Alt. on A scale and Y/X at the are 16 on the A scale (or vice versa).

The choice of the most convenient method for the calculation given above may be determined by rapid inspection. For multiplication: Swing the arm up from the horizontal position until a factor (X or Y) falls either (a) on Are C, or (b) on Alt, whichever requires a smaller upward swing. If (a), use multiplication Method A above; if (b), use multiplication Method B. For division: If the positions of X and Y (on their respective scales) are not widely separated, division Method C above is the most conveniente.g., in the case of 70/ 60 or 23/75. If they are widely separated then division Method A will be used it Y is towards the right end of the scales-cg, 50/90and division Method B will be used when Y is nearer the left end of the scalese.g., 60/12. Selection of the upper or lower scales for the answers and the placing of Zeros or decimal points will be determined from the rough magnitudes involved (as in slide-rule use).

3. To find the square of X Swing X on the A scale to coincide with are 16 and read X on upper D scale below X. Alternatively, swing X on the A scale to coincide with Alt, and read X on the A scale above X on the D scale.

4. To find the square root or" X- Place H at X on upper D scale, swing A scale to juncture of H and 16, and read answer at 16 on the A scale. FIG. 2 illustrates the determination '9=the square root of 81, and also that 8l=the square of 9 using the H line.

I claim:

1. A scale type calculator comprising a body having a fiat surface carrying across its lower extent upper and lower contiguously parallel linear base scales, an altitude 4. line extending normal to said scales, a transparent arm pivotally mounted on said body at one end of said base scales and carrying along its length outer and inner contignously parallel linear arm scales, said base and arm scales being the same and each comprising differently divided and numbered individual scales having progressively numbered equal divisions and numerically related so that the reading at any point along one scale is the square root of ll) times the corresponding reading on the contiguous scale, the pivot point of the arm being such that when brought into parallelism the arm and base scales have the same values at points of alinement normal thereto, said body carrying an arc intersectable with said pivot point and having its diameter along the arm scales when the latter scales are parallel to the base scales, said arc being progressively intersectable by the arm scales at varying angles by swinging the arm to selected scale values, and means movable parallel to the base scales and carrying an altitude line normal thereto and intersectable with said arm scales at diiferent positions of the 2. A calculator according to claim 1, in which said body has a semi circular periphery about and spaced from said are.

3. A calculator according to claim 1, in which one each of said arm and base scales divides the arc diameter length into equal numbered divisions of 100.

4. A calculator according to claim 1, in which the outer arm scale and upper base scale divide the arc diameter length into equal numbered divisions of 100 which are the square root of 10 times the corresponding values on the contiguous scales.

5. A calculator according to claim 4, in which the first mentioned altitude line intersects said arc and base scale at a location corresponding to 10 on its lower numbered scale.

6. A calculator according to claim 1, in which the interval lines on the arm scales extend diagonally of the longitudinal extent of the scales.

7. A calculator according to claim 1, in which said base scales are carried on a raised strip area of the body having its edge engagea le by the arm when its scales are swung parallel to the base scales.

8. A calculator according to claim 1, in which said al itude line carrying means comprises a member slidable along a guide edge of the body parallel to said base scales and having a transparent arm carrying the last mentioned altitude line.

9. A calculator according to claim 8, in which said guide edge is below the base scales.

10. A calculator according to claim 8, in which said guide edge is between the arm and base scales.

11. A calculator according to claim 8, in which said member is pivotally carried by the bod Graham June 30, 1959 Gabriel 

1. A SCALE TYPE CALCULATOR COMPRISING A BODY HAVING A FLAT SURFACE CARRYING ACROSS ITS LOWER EXTENT UPPER AND LOWER CONTIGUOUSLY PARALLEL LINEAR BASE SCALES, AN ALTITUDE LINE EXTENDING NORMAL TO SAID SCALES, A TRANSPARENT ARM PIVOTALLY MOUNTED ON SAID BODY AT ONE END OF SAID BASE SCALES AND CARRYING ALONG ITS LENGTH OUTER AND INNER CONTIGUOUSLY PARALLEL LINEAR ARM SCALES, SAID BASE AND ARM SCALES BEING THE SAME AND EACH COMPRISING DIFFERENTLY DIVIDED AND NUMBERED INDIVIDUAL SCALES HAVING PROGRESSIVELY NUMBERED EQUAL DIVISIONS AND NUMERICALLY RELATED SO THAT THE READING AT ANY POINT ALONG ONE SCALE IS THE SQUARE ROOT OF 10 TIMES THE CORRESPONDING READING ON THE CONTIGUOUS SCALE, THE PIVOT POINT OF THE ARM BEING SUCH THAT WHEN BROUGHT INTO PARALLELISM THE ARM AND BASE SCALES HAVE THE SAME VALUES AT POINTS OF ALINEMENT NORMAL THERETO, SAID BODY CARRYING AN ARC INTERSECTABLE WITH SAID PIVOT POINT AND HAVING ITS DIAMETER ALONG THE ARM SCALES WHEN THE LATTER SCALES ARE PARALLEL TO THE BASE SCALES, SAID ARC BEING PROGRESSIVELY INTERSECTABLE BY THE ARM SCALES AT VARYING ANGLES BY SWINGING THE ARM TO SELECTED SCALE VALUES, AND MEANS MOVABLE PARALLEL TO THE BASE SCALES AND CARRYING AN ALTITUDE LINE NORMAL THERETO AND INTERSECTABLE WITH SAID ARM SCALES AT DIFFERENT POSITIONS OF THE ARM. 